Upper Bound on the Packing Density of Regular Tetrahedra and Octahedra

Aristotle contended that (regular) tetrahedra tile space, an opinion that remained widespread until it was observed that non-overlapping tetrahedra cannot subtend a solid angle of 4π around a point if this point lies on a tetrahedron edge. From this 15th century argument, we can deduce that tetrahedra do not tile space but, more than 500 years later, we are unaware of any known non-trivial upper bound to the packing density of tetrahedra. In this article, we calculate such a bound. To this end, we show the existence, in any packing of regular tetrahedra, of a set of disjoint spheres centered on tetrahedron edges, so that each sphere is not fully covered by the packing. The bound on the amount of space that is not covered in each sphere is obtained in a recursive way by building on the solid angle argument. The argument can be readily modified to apply to other polyhedra. The resulting lower bound on the fraction of empty space in a packing of regular tetrahedra is 2.6…×10⁻²⁵ and reaches 1.4…×10⁻¹² for regular octahedra.     

Cyclo[2]benzimidazole: luminescence turn-on sensing of anions

Cyclo[2]benzimidazole is a new host for anions that turns on its luminescence up to 150 fold upon binding. Photoexcited cyclo[2]benzimidazole undergoes an efficient non-radiative deactivation through an excited-state intramolecular proton-transfer (ESIPT) mechanism. Upon binding an anion, the ESIPT pathway is blocked, resulting in an increase in the luminescence efficiency.     

On completely reducible solvable subgroups of GL(n, Δ)

Let Δ be a finite field and denote by GL(n, Δ) the group ofn×n nonsingular matrices defined over Δ. LetR⊆GL(n, Δ) be a solvable, completely reducible subgroup of maximal order. For |Δ|≧2, |Δ|≠3 we give bounds for |R| which improve previous ones. Moreover for |Δ|=3 or |Δ|>13 we determine the structure ofR, in particular we show thatR is unique, up to conjugacy. This work is part of a Ph.D. thesis done at the Hebrew University under the supervision of Professor A. Mann.     

A−2 production in π−p interactions at 3.9 GeV/c

The reaction π^?p → A^?₂p at 3.9 GeV/c incident momentum is studied using data corresponding to the ?^°π^?, ηπ^? and K^δ_sK^? decay modes of the A^?₂. Unnatural parity exchange is found to be important at this energy. The natural parity exchange component of the differential cross section exhibits structure at t′ ≈ GeV².     

Reversible and persistent electrical bistability in single crystals of a self-assembled pi-conjugated tetraaryl system: a submicrometer scale electrical characterization

A new pi-conjugated electroactive 4,4'-bipyridinium that bears two pyridazone self-complementary units was prepared and characterized. The new system readily assembles and forms at least two stable charge-transfer crystalline structures having a thermal population of unpaired electrons. The crystals of one phase exhibit electrical bistability, displaying either high (ON) and low (OFF) conductivity, at the same applied bias, depending on the electrical history of the system. The relation between the supramolecular structure of the crystals and their electrical properties is also discussed.     

Finite temperature SU(2) lattice gauge theory

We discuss SU(2) lattice gauge theories at non-zero temperature and prove several rigorous results including i) the absence of confinement for sufficiently high temperature in the pure gauge theory, and ii) the absence of spontaneous chiral symmetry breaking for sufficiently high temperature in the theory with massless fundamental representation fermions.     

Highly confined hybrid spoof surface plasmons in ultrathin metal-dielectric heterostructures

Highly confined "spoof" surface plasmons (SSPs) are theoretically predicted to exist in a perforated metal film coated with a thin dielectric layer. Strong modes confinement results from the additional waveguiding by the layer. Spectral characteristics, field distribution, and lifetime of these SSPs are tunable by the holes' size and shape. SSPs exist both above and below the light line, offering two classes of applications: "perfect" far-field absorption and efficient emission into guided modes. It is experimentally shown that these plasmonlike modes can turn thin, weakly absorbing semiconductor films into perfect absorbers.     

Toward the abelian root groups conjecture for special Moufang sets

We prove that if a root group of a special Moufang set contains an element of order then it is abelian.     

Phase-separation transition in liquid mixtures near curved charged objects

We study the thermodynamic behavior of nonpolar liquid mixtures in the vicinity of curved charged objects, such as electrodes or charged colloids. There is a critical value of charge (or potential), above which a phase-separation transition occurs, and the interface between high- and low-dielectric constant components becomes sharp. Analytical and numerical composition profiles are given, and the equilibrium front location as a function of charge or voltage is found. We further employ a simple Cahn-Hilliard type equation to study the dynamics of phase separation in spatially nonuniform electric fields. We find an exponential temporal relaxation of the demixing front location. We give the dependence of the steady-state location and characteristic time on the charge, mixture composition and ambient temperature.